(x+2)(x+3)/(x-2) >= 0 are less than 5?

Hi rsarashi,

While this question looks a bit complex, it's not as difficult as it might appear. This question emphasizes a particular part of the process that is so important for GMAT questions of all types: you have to take notes and do work in an organized way.

In this prompt, we're asked to focus on integer solutions that are LESS than 5. From the answers, we know that there is at least one solution, but no more than five solutions. This means that there aren't that many options and they shouldn't be too hard to find.

If you were "stuck" on this question, then here's how you can go about solving it quickly - Just start plugging in integers until you've "found" all of the ones that "fit." Start with the number 4, then 3, etc. You'd be amazed how often you can use what's called "brute force" against a Quant question; plug in numbers and pound on the question until you've found the solution.

GMAT assassins aren't born, they're made,
Rich

rsarashi wrote:How many of the integers that satisfy the inequality (x+2)(x+3)/(x-2) >= 0 are less than 5?

A. 1
B. 2
C. 3
D. 4
E. 5

OAD

Hi rsarashi,

Let's observe the inequality (x+2)(x+3)/(x-2) >= 0 and derive results.

1. Since @ x= 2, the denominator (x-2) would become 0, making the inequality undefines, it is not a solution.

2. We see that @ x = 3 and @ x = 4, the numerator (x+2)(x+3), as well as the denominator (x-2) would remain positive, thus x = 3 and x= 4 are two solutions.

3. Let's focus on x < 2 values. Since @ x = 1 or 0 or -1, the numerator (x+2)(x+3) remain positive, the denominator (x-2) becomes negative, making the inequality negative, which is not we want. The inequality >= 0. Thus, x = 1 or 0 or -1 are not the solutions.

4. We see that @ x= -2 and @ x= -3, inequality turns 0, thus these two are the solutions.

5. We must not focus on x < -3 since @x<-3, the numerator (x+2)(x+3) remain positive (negative*negative = positive), the denominator (x-2) becomes negative, making the inequality negative, which is not we want.

So, there are four numbers of integer solutions that are less than 5: x = -3, -2, 3 and 4.

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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